Number...3 A A Aa-Jabx X, X¹² A-ay-A-DS-12Font2.re to search3.5MEParagraphStylesLet Y₁, Y2, Y3, Y4, Ys and X1, X2, X9 be independent and normally distributed random samplesfrom populations with means ₁ = 2 and 2 = 8 and variances 01²=5 and 02²= k, respectively.Suppose that P(X-Y> 10) = 0.02275, find the value of ₂² = k6.DIK ENGLISH (SOUTH AFRICA)Suppose that Y1, Y2, Ym and X1, X2, ..., Xm are independent normally distributed random samplesfrom populations with means ₁ and ₂ and variances 01² and 022, respectively. IsX-Y a consistent estimator of 2-₁? Justify your answer.4. Suppose that Y₁, Y2,... Ym is a random sample of size m from Gamma(a = 3, B = 0), where is notknown Check whether or not the maximum likelihood estimator is a minimum variance unbiasedestimator of the parameter oAaBbCcDc AaBbCcDc AaBbC AaBbCct AaB AaBbcct AaBbCcDT Normal 1 No Spac... Heading 1 Heading 2TitleSubtitle Subtle Em..0550Suppose that a random sample X1, X2, X20 follows an exponential distribution with parameter pCheck whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)%91confidence interval for p.Suppose that a random sample x is given by a probability density function(B-2), 0

Answered: 3. Suppose that Y1, Y2, Ym and X₁, X2,…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 5E: Population Genetics In the study of population genetics, an important measure of inbreeding is the...

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Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

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3. Suppose that Y1, Y2, Ym and X₁, X2, ..., Xm are independent normally distributed random samples from populations with means ₁ and 2 and variances 1² and 02², respectively. Is X - Y a consistent estimator of 2-₁? Justify your answer.